It's the squad's third defeat in the last three matches.
The Robins' first victory in six matches moved them back into the League Two play-off positions.
Latics started brightly and had a few half-chances in the opening ten minutes, the best effort of this period was by David Jones as he intercepted a ball inside the hosts’ half and played a one-two with Scott Wilson and shot from the edge of the area, but Scott Flinders was able to catch the strike.
Sheaf struck in the 32nd minute, finishing well after Tahvon Campbell's pull-back from the left. It was the first EFL goal of the Hull loanee's career.
Campbell was denied by Zeus de la Paz after running through one-on-one after a pass from Sheaf, then May had the ball in the net five minutes before the break but it was disallowed for handball.
Cheltenham pressed for a second after half-time, but their experienced goalkeeper Scott Flinders was carried off on a stretcher after a collision with Scott Wilson in the 57th minute.
May made it 2-0 in the 76th minute after more good work from Campbell, firing in from close range after his initial effort was blocked.
Substitute goalkeeper Rhys Lovett made the save of the match to keep out a powerful strike from Oldham substitute Chris Eagles.
Broom added the third deep into time added on after Sean Long's pass.
